Statistical analysis of the eigenfunctions of the Anderson tight-binding model with on-site disorder on regular random graphs strongly suggests that the extended states are multifractal at any finite disorder. The spectrum of fractal dimensions $f(al
pha)$ defined in Eq.(3), remains positive for $alpha$ noticeably far from 1 even when the disorder is several times weaker than the one which leads to the Anderson localization, i.e. the ergodicity can be reached only in the absence of disorder. The one-particle multifractality on the Bethe lattice signals on a possible inapplicability of the equipartition law to a generic many-body quantum system as long as it remains isolated.
The middle-aged PSR J0357+3205 is a nearby, radio-quiet, bright gamma-ray pulsar discovered by the Fermi mission. Our previous Chandra observation revealed a huge, very peculiar structure of diffuse X-ray emission, originating at the pulsar position
and extending for > 9 on the plane of the sky. To better understand the nature of such a nebula, we have studied the proper motion of the parent pulsar. We performed relative astrometry on Chandra images of the field spanning a time baseline of 2.2 yr, unveiling a significant angular displacement of the pulsar counterpart, corresponding to a proper motion of 0.165+/-0.030 yr^(-1). At a distance of ~500 pc, the space velocity of the pulsar would be of ~390 km s^(-1) assuming no inclination with respect to the plane of the sky. The direction of the pulsar proper motion is perfectly aligned with the main axis of the X-ray nebula, pointing to a physical, yet elusive link between the nebula and the pulsar space velocity. No optical emission in the H_alpha line is seen in a deep image collected at the Gemini telescope, which implies that the interstellar medium into which the pulsar is moving is fully ionized.
RX J0822-4300 is the Central Compact Object associated with the Puppis A supernova remnant. Previous X-ray observations suggested RX J0822-4300 to be a young neutron star with a weak dipole field and a peculiar surface temperature distribution domina
ted by two antipodal spots with different temperatures and sizes. An emission line at 0.8 keV was also detected. We performed a very deep (130 ks) observation with XMM-Newton, which allowed us to study in detail the phase-resolved properties of RX J0822-4300. Our new data confirm the existence of a narrow spectral feature, best modelled as an emission line, only seen in the `Soft phase interval - when the cooler region is best aligned to the line of sight. Surprisingly, comparison of our recent observations to the older ones yields evidence for a variation in the emission line component, which can be modelled as a decrease in the central energy from ~0.80 keV in 2001 to ~0.73 keV in 2009--2010. The line could be generated via cyclotron scattering of thermal photons in an optically thin layer of gas, or - alternatively - it could originate in low-rate accretion by a debris disk. In any case, a variation in energy, pointing to a variation of the magnetic field in the line emitting region, cannot be easily accounted for.
The Large Area Telescope (LAT) onboard the Fermi satellite opened a new era for pulsar astronomy, detecting gamma-ray pulsations from more than 60 pulsars, ~40% of which are not seen at radio wavelengths. One of the most interesting sources discovere
d by LAT is PSR J0357+3205, a radio-quiet, middle-aged (tau_C ~0.5 Myr) pulsar standing out for its very low spin-down luminosity (Erot ~6x10^33 erg/s), indeed the lowest among non-recycled gamma-ray pulsars. A deep X-ray observation with Chandra (0.5-10 keV), coupled with sensitive optical/infrared ground-based images of the field, allowed us to identify PSR J0357+3205 as a faint source with a soft spectrum, consistent with a purely non-thermal emission (photon index Gamma=2.53+/-0.25). The absorbing column (NH=8+/-4x10^20 cm^-2) is consistent with a distance of a few hundred parsecs. Moreover, the Chandra data unveiled a huge (9 arcmin long) extended feature apparently protruding from the pulsar. Its non-thermal X-ray spectrum points to synchrotron emission from energetic particles from the pulsar wind, possibly similar to other elongated X-ray tails associated with rotation-powered pulsars and explained as bow-shock pulsar wind nebulae (PWNe). However, energetic arguments, as well as the peculiar morphology of the diffuse feature associated with PSR J0357+3205 make the bow-shock PWN interpretation rather challenging.
Prompted by the Fermi LAT discovery of a radio-quiet gamma-ray pulsar inside the CTA 1 supernova remnant, we obtained a 130 ks XMM-Newton observation to assess the timing behavior of this pulsar. Exploiting both the unprecedented photon harvest and t
he contemporary Fermi LAT timing measurements, a 4.7 sigma single peak pulsation is detected, making PSR J0007+7303 the second example, after Geminga, of a radio-quiet gamma-ray pulsar also seen to pulsate in X-rays. Phase-resolved spectroscopy shows that the off-pulse portion of the light curve is dominated by a power-law, non-thermal spectrum, while the X-ray peak emission appears to be mainly of thermal origin, probably from a polar cap heated by magnetospheric return currents, pointing to a hot spot varying throughout the pulsar rotation.
Central Compact Objects (CCOs) are a handful of soft X-ray sources located close to the centers of Supernova Remnants and supposed to be young, radio-quiet Isolated Neutron Stars (INSs). A clear understanding of their physics would be crucial in orde
r to complete our view of the birth properties of INSs. We will review the phenomenologies of CCOs, underlining the most important, recent results, and we will discuss the possible relationships of such sources with other classes of INSs.
PSR B0540-69 is the Crab twin in the Large Magellanic Cloud. Age, energetic and overall behaviour of the two pulsars are very similar. The same is true for the general appearance of their pulsar wind nebulae (PWNe). Analysis of Hubble Space Telescope
images spanning 10 years unveiled significant variability in the PWN surrounding PSR B0540-69, with a hot spot moving at ~0.04c. Such behaviour, reminiscent of the variability observed in the Crab nebula along the counter-jet direction, may suggest an alternative scenario for the geometry of the system. The same data were used to assess the pulsar proper motion. The null displacement recorded over 10 y allowed us to set a 3sigma upper limit of 290 km/s to the pulsar velocity.
